# [seqfan] Re: The name of A053810

Arthur O'Dwyer arthur.j.odwyer at gmail.com
Fri Nov 3 14:18:42 CET 2023

```On Fri, Nov 3, 2023 at 9:00 AM Felix Fröhlich <felix.froe at gmail.com> wrote:

> Dear SeqFans,
> to me, the definition of A053810 sounds strange. The first comment in
> A000961 says "The term prime power is ambiguous. To a mathematician it
> means any number p^k, p prime, k >= 0, including p^0 = 1". This seems to
> suggest that the "... of prime numbers" part in the definition of A053810
> is redundant. The PARI code seems to suggest that the actual definition is
> "Prime-th powers of prime numbers". Maybe the name could be written more
> clearly as "Prime powers with prime exponents", or, perhaps, "Powers of
> prime numbers with prime exponents".
>
> As this is an old sequence I want to discuss this possible change first.
>

I think there are several defects in this area.
- A000961's first comment "The term prime power is ambiguous" is silly IMO.
"To a mathematician it means..." the thing it means, right? To a
non-mathematician, I don't think it means anything (and OEIS wouldn't care
the current title. But the second comment — that it's debatable whether 1
should count as a prime power — is useful, and in particular the fact
that A246655 is the same as A000961 without "1" needn't be a parenthetical.
- A053810's first comment "This is to triprimes..." is here by mistake; it
has been transposed from A217784 (where it belongs).
- A053810's actual title should be "Primes to prime powers," by analogy
to A113877 and A217784.
- Consider whether all three sequences' titles should have the word
"raised" added: "Primes *raised* to prime powers," "Semiprimes *raised* to
semiprime powers," "Triprimes *raised* to triprime powers." That might
lighten the heavy lifting currently being done by the small word "to".

–Arthur
```